Multiple doubly periodic solutions of semilinear dissipative hyperbolic equations
type: Item
instance of: scholarly article
title: Multiple doubly periodic solutions of semilinear dissipative hyperbolic equations
zbMATH Open document ID: 0870.35069
author: Wan Se Kim
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-07-14T00:00:00Z
review text: The author extends some generalized Ambrosetti-Prodi-type conditions obtained for ordinary differential equations by Fabry, Mawhin, Nkashama and Ding, to the weak doubly periodic solutions of semilinear hyperbolic equations of the form \[ \beta u_t+ u_{tt}- u_{xx}+ g(t,x,u)= s+h(t,x), \] with \(\beta\neq 0\), \(\iint h(t,x)dt dx=0\), \(g\) has at most linear growth in \(|u|\), \(g\) is nonnegative and \(\lim_{|u|\to\infty} g(t,x,u)= +\infty\) uniformly in \((t,x)\). The proofs use topological degree arguments and delicate estimates.
Mathematics Subject Classification ID: 35L70
Mathematics Subject Classification ID: 47H11
Mathematics Subject Classification ID: 35B10
zbMATH DE Number: 902469
zbMATH Keywords: telegraph equation
zbMATH Keywords: Ambrosetti-Prodi-type conditions
zbMATH Keywords: topological degree arguments
reviewed by: Jean Mawhin
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0049
OpenAlex ID: W2068294414
DOI: 10.1006/JMAA.1996.0049
Recommended article: Q4343528
Recommended article: Multiplicity results for periodic solutions of semilinear dissipative hyperbolic equations with coercive nonlinear term
Recommended article: Double-periodic boundary value problem for nonlinear dissipative hyperbolic equations
Recommended article: On doubly periodic solutions of nonlinear hyperbolic partial differential systems
Recommended article: Q3816436
Recommended article: Multiplicity result for semilinear dissipative hyperbolic equations
Recommended article: Q4518254
Recommended article: Q3818705
Recommended article: Q4235080
Recommended article: Existence of Multiple Periodic Solutions for a Semilinear Evolution Equation
description: scientific article; zbMATH DE number 902469